The club has faced sustained pressure over a speech chief executive Matthew Pavlich delivered before the Sydney-Carlton opening round match at the SCG on March 5.
The address paid tribute to victims of the Bondi terrorist attack but did not directly mention the Jewish community, with references removed from an earlier version of the script.
Following days of speculation the AFL was responsible for the script change, the Swans released a statement on Monday taking full accountability for the decision.
"There was no directive or instruction from the AFL to remove or change the reference to the Jewish community in the script," the statement said.
"That script change was made within our club in a genuine effort to use inclusive language by referring to the 'whole community'."
The club said the focus of the speech was to recognise those present on the field at the time, including members of the Jewish community, heroic bystanders and first responders.
"We acknowledge that was an error of judgment and again we apologise," it said, reiterating its support for the Jewish community.
The Swans' admission takes pressure off the AFL, which Liberal senator James Paterson on Monday referred to the anti-Semitism royal commission to investigate the circumstances surrounding the script change.
"It is incredibly disappointing to learn that someone at an AFL club believes it was inclusive to remove all references to Jews in a script about the anti-Semitic Bondi terror attack, whose victims were overwhelmingly Jewish," he told AAP.
"It is further evidence of deeply ingrained cultural problems in our sporting institutions that must be probed thoroughly by the royal commission."
Senator Paterson has asked former High Court judge Virginia Bell, who is leading the royal commission, to request the AFL preserve all documents and communications relating to the matter, including any correspondence with the Sydney Swans.
The issue was first raised on Friday by media commentator and AFL great Gerard Healy, who claimed the initial script was changed to remove the word "Jew" and references to the Jewish community.
Sydney Swans chairman Andrew Pridham apologised for the omission on Saturday night at a function before the Swans' round-one clash with the Brisbane Lions.
"This was not intentional. We apologise for this omission. It was a Sydney Swans initiative, and a Swans-led event, and we take full responsibility," he said.
"The tribute was a genuine attempt to show compassion to everyone impacted by the terrible events on 14 December, and most of all the Jewish community."
It followed comments from AFL chief executive Andrew Dillon, who on Saturday failed to clarify whether the league played a role in the change of script.
"I don't know the ins and outs of scripts," Dillon said on SEN radio, reinforcing his support for the Jewish community.
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